The sometime political ally of Mr Cameron accused the Prime Minister of “inaccurate” comments about cuts after receiving a complaint about plans to slash vital services.

The PM, who represents a local constituency in Oxfordshire as an MP, had written to the council leader to complain about proposed cuts to frontline services in his own area – including elderly day centres, museums, and libraries.

He claimed that the council should be making “back-office savings” and protecting frontline services, that spending had increased in the authority in recent years, and that he was “disappointed” in cuts.

Mr Hudspeth wrote back to explain the council’s budget situation to the PM, who appeared unaware that cuts to local authorities would mean significant reductions to frontline local services.

“Excluding schools, our total government grants have fallen from £194m in 2009/10 to £122m a year in 2015/16, and are projected to keep falling at a similar rate,” the council leader said.

“I cannot accept your description of a drop in funding of £72m or 37% as a ‘slight fall’.”

The Conservative councillor also explained that an assertion by the PM that only £204m in cuts had been made in the local area was in fact wrong and that £626m had in fact been cut.

He said a suggestion by the PM that excess council property be sold off to fund services as a “creative” solution “neither legal, nor sustainable in the long-term since they are one-off receipts”.

Oxfordshire’s desperate budget situation comes despite it being one of the most wealthy counties in the UK.

An analysis by the Institute for Fiscal Studies released before the general election found that cuts to council budgets were sharpest in the UK’s poorest areas.

Inner-city boroughs like Tower Hamlets have lost out by 42.1 per cent since 2010 while leafier areas like north-east Lincolnshire escaped with reductions as low as 6.3 per cent – still a difficult reduction to make in the context of rising elderly social care costs.

Figures collated by Labour over the summer found that the 10 most deprived councils were facing cuts 18 times higher than that of the 10 richest councils.

A spokesperson for David Cameron said: “There is still significant scope for sensible savings across local government to be made by back office consolidation, disposing of surplus property and joining up our local public services; we will be discussing with Oxfordshire how this can be taken forward to help protect frontline services.”

Mr Hudspeth told the same newspaper he did not want to comment on leaked private correspondence not meant for publication.